Furnace apparatus utilizing a resultant magnetic field or fields produced by mutual interaction of at least two independently generated magnetic fields and methods of operating an electric arc furnace

ABSTRACT

In a furnace having an electric arc extending between an electrode and material to be melted which is composed at least partially of conductive material, a resultant magnetic field having a desired field configuration is produced by mutual interaction of two or more separately and independently generated magnetic fields and the resultant magnetic field is utilized to improve furnace operation in a number of ways. In some embodiments, two fields are generated, one by a field coil in the tip of the electrode and one by a coil at or near the wall of the furnace, which latter coil may be a solenoid having a length to diameter ratio equal to or greater than one or a concentrated coil having a length to diameter ratio substantially less than one, and the resultant field has a configuration which may increase or improve arc-moving forces on the arc provided to reduce erosion of material from the electrode by arc action thereon, or may improve focusing of the arc between electrode and melt, or may improve control of a diffused arc, or may improve stirring of the melt, or may control the portion of the surface of the melt to which the arc strikes, or may prevent arc flares to the wall of the furnace, or may prevent glow discharges, or may increase feed rate, or may improve grain structure in an ingot produced, or may include any combination of the aforementioned and other improvements. In another embodiment, three magnetic fields are separately generated, one by an electric tip field coil, one by a solenoid and one by a concentrated coil adjacent the solenoid and having an axially adjustable position thereon. In a further embodiment, two magnetic fields are separately generated by two field generating means external to the electrode and under some conditions no interacting magnetic field is generated within the electrode. In other embodiments, two electrodes are mounted in the furnace each with an arc extending therefrom to the melt, and three electrodes are mounted in the furnace each with an arc extending therefrom to the melt. New and improved processes and methods of furnace operation are also described.

United States Patent [191 Akers Feb. 19, 1974 1 FURNACE APPARATUS UTILIZING A RESULTANT MAGNETIC FIELD OR FIELDS PRODUCED BY MUTUAL INTERACTION OF AT LEAST TWO INDEPENDENTLY GENERATED MAGNETIC FIELDS AND METHODS OF OPERATING AN ELECTRIC ARC FURNACE [75] Inventor: Ronald R. Akers, Trafford, Pa.

[73] Assignee: Westinghouse Electric Corporation,

Pittsburgh, Pa.

22 Filed: Sept. 22, 1972 21 Appl. No.: 291,433

Primary ExaminerRoy N. Envall, Jr. Attorney, Agent, or Firm-M. J. Moran [57] ABSTRACT In a furnace having an electric arc extending between an electrode and material to be melted which iscomposed at least partially of conductive material, a resultant magnetic field having a desired field configuration is produced by mutual interaction of two or more separately and independently generated magnetic fields and the resultant magnetic field is utilized to improve furnace operation in a number of ways. In some em bodiments, two fields are generated, one by a field coil in the tip of the electrode and one by a coil at or near the wall of the furnace, which latter coil may be a solenoid having a length to diameter ratio equal to or greater than one or a concentrated coil having a length to diameter ratio substantially less than one, and the resultant field has a configuration which may increase or improve arc-moving forces on the are provided to reduce erosion of material from the electrode by arc action thereon, or may improve focusing of the arc between electrode and melt, or may improve control of a diffused arc, or may improve stirring of the melt, or may control the portion of the surface of the melt to which the arc strikes, or may prevent arc flares to the wall of the furnace, or may prevent glow discharges, or may increase feed rate, or may improve grain structure in an ingot produced, or may include any combination of the aforementioned and other improvements. In another embodiment, three magnetic fields are separately generated, one by an electric tip field coil, one by a solenoid and one by a concentrated coil adjacent the solenoid and having an axially adjustable position thereon. In a further embodiment, two magnetic fields are separately generated by two field generating means external to the electrode and under some conditions no interacting magnetic field is generated within the electrode. In other embodiments, two electrodes are mounted in the furnace each with an are extending therefrom to the melt, and three electrodes are mounted in the furnace each with an arc extending therefrom to the melt. New and improved processes and methods of furnace operation are also described.

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FURNACE APPARATUS UTILIZING A RESULTANT MAGNETIC FIELD OR FIELDS PRODUCED BY MUTUAL INTERACTION OF AT LEAST TWO INDEPENDENTLY GENERATED MAGNETIC FIELDS AND METHODS OF OPERATING AN ELECTRIC ARC FURNACE CROSS-REFERENCE TO RELATED APPLICATIONS This application is related to the copending application Ser. No. 291,466, filed concurrently by RA. Akels, A.R. Vaia, F.A. Azinger and CB. Wolf, and Ser. No. 291,470, filed concurrently by Frank J. Kolano, both of which are assigned to the same assignee as the present invention.

BACKGROUND OF THE INVENTION 1. Field of the Invention The field of the invention relates to improvements in the performance of electric arc melting apparatus, in which an arc takes place from an electrode to a melt, and is concerned with improving performance in a large number of ways by generating two magnetic fields within the furnace at least one of which extends at least partially through the melt and the portion of the volume of the furnace which includes the electrode tip, the separately generated magnetic fields interacting with each other to provide a resultant magnetic field which gives improved performance.

The invention is concerned with are movement on the electrode to reduce erosion, are focusing, control of the area of the pool on which the arc impinges, stirring the melt, increasing the feed rate, preventing arc flare, preventing glow discharges, providing increased heating efficiency, providing for better grain structure and greater homogeneity in an ingot produced, and improvement in operation in a diffused-arc mode.

2. Discussion of the Prior Art It is known to use an electrode with means only in the tip or adjacent the tip for setting up a magnetic field transverse to the arc current path which exerts a force on the are which causes the arc to move substantially continuously in generally repetitive paths around the arcing surface of the electrode; such an electrode is shown in US. Pat. No. 3,369,067, issued to S. M. DeCorso for Nonconsumable Annular Fluid-Cooled Electrode for Arc Furnaces, and US. Pat. No. 3,385,987, issued to C. B. Wolf et al. for Electrode for an Arc Furnace Having a Fluid-Cooled Arcing Surface and a Continuously Moving Arc Thereon, both of said patents being assigned to the assignee of the instant invention.

It is also known in the art to utilize only an external field generating means to generate a magnetic field within a furnace, with a portion of the field extending through the melt and a portion of the field occupying at least part of the remaining volume of the furnace and existing in the area of a carboniferous or consumable electrode usually axially mounted in the furnace, and in the area between electrode and melt. U.S. Pat. No. 2,727,937, issued to Boyer constitutes part of the prior art.

It is also old in the art to use a single magnetic field generating means to interact with an are between a rotating electrode and the melt, such that the field reacts with the arc to cause it to move in a direction opposite the direction of rotation as shown in US. Pat. No. 3,597,519, issued to G. A. Kemeny and R. A. Akers entitled Magnetic-Field Rotating-Electrode Electric Arc Furnace Apparatus and Methods.

The applicant has used several years ago a combination in an arc furnace in which two magnetic field producing means are used to control an arc. The specific magnetic field producing means used by the applicant in the past comprised using a relatively short electrode tip magnet having 3,200 ampere turns of magnetomotive force available and a solenoid having 5,040 ampere turns of bucking or opposing magnetomotive force available, the magnetic fields produced by these forces being specifically arranged to cancel at one point along the centerline of the electric arc furnace in which this apparatus was being used. The relationship between the sources of magnetic fields or the generators of magnetomotive force were such that the net or resultant megnetic field strengths at the electrode tip was provided primarily by the electrode tip field coil rather than the solenoid even though the magnetomotive force generated by the electrode tip magnet was relatively smaller than the magnetomotive force of the solenoid. This generated a balanced resultant magnetic field near the electrode surface most conducive to faster arc rotation and less surface wear or erosion on the electrode. In the latter balanced field systems the field strength of the solenoid is more nearly equal to the field strength of the tip coil than in embodiments of disclosed inventions described hereinafter.

SUMMARY OF THE INVENTION In electric arc furnace apparatus of the type in which an arc takes place between an electrode and a melt, two magnetic fields are separately generated within at least a portion of the volume of the furnace to produce a resultant magnetic field configuration which accomplishes certain desirable results with respect to the electrode, the melt, and the associated arc, and accomplishes certain other desirable results with respect to the melt and the feed rate of material to the melt. In some embodiments, two magnetic fields are generated, one by a solenoid adjacent the wall of the furnace, the field extending at least a substantial distance below the level of the melt and extending at least a substantial distance above the position of the electrode tip, and the other magnetic field is generated by a compact and relatively short field coil, the winding of which is composed of many layers, at least one of the two abovementioned field coils being slidable so that its axial position with respect to the melt and/or the other field coilis adjustable, to provide a wide variety of desired resultant magnetic field configurations. In other embodiments, the resultant magnetic field is produced by a coil in the electrode tip interacting with an externally generated field produced either by a solenoid or a compact coil or both. The tip field and the net external field may be in polarity adding or polarity opposition at the axis of the electrode tip; in the latter case, in accordance with the relative strengths of the two fields, the magnetic field lines may extend substantially uniformly around the entire arcing surface of the electrode and, where the arc is in a restricted mode, greatly enhance the ability of the magnetic field to continuously move the arc in repetitive paths around the arcing surface, and while the arc is in a diffused mode, to move the diffused discharge over the arcing surface. If the fields are in the magnetic polarity opposition mode, as the relative strength of the field generated in the tip is increased with respect to the strength of an externally generated field, the magnetic field around the arcing surface of the tip may include some field lines which extend to and into the adjacent surface of the melt; under some conditions, the central portion of the melt may rotate in one direction, while the remainder of the melt is caused to rotate in the opposite direction as a result of the externally produced magnetic field while the fields are in opposition, thereby providing better stirring of the melt.

Where the polarity of the magnetic field generated in the tip is such that it is not in opposition to the externally produced magnetic field but is in polarity adding, a resultant magnetic field is produced adjacent the tip which may have a component which exerts a relatively small rotating force on the arc and additionally effectively focuses the are between the electrode and the melt and provides control of the are so that it does not flare outwardly to the wall of the furnace or slant between electrode and melt; stirring of the melt may be enhanced.

Further summarizing the invention, including magnetic fields selectively in polarity adding or in opposition, in a number of areas which include positioning, controlling, focusing, or moving an are between an electrode and a melt, my invention permits a greatly increased feed rate of material to the melt, produces increased heating efficiency in the melt, gives better stirring, gives improved grain structure to ingots, and provides for are control to reduce erosion. lngots can be formed from magnetic materials with acceptable grain structure even though portions of the ingot are cooled during the ingot-forming process below the Curie temperature.

It has been found by experiment that my apparatus can, under certain conditions, including the use of a vacuum furnace, substantially reduce the pressure at which the arc goes into glow, and also permit a greater arc length. With fields in opposition and operating with an arc length of one inch, it was found that while arcing to graphite the arc went into glow discharge in the 0700-0800 torr pressure range.

When the fields were changed to magnetic polarity adding, it was found that the pressure in the furnace could be reduced to 0.25 millitorr before glow discharge occurred, and at 0.06 torr the arc length could be increased to three inches.

In some embodiments, the two magnetic fields are produced by a solenoid adjacent the furnace wall or the mold or crucible and a concentrated coil with a magnetic yoke adjacent the solenoid and having positions axially adjustable with respect to the solenoid so that the. fields mutually interact as desired and a resultant field having a desired configuration is produced. In other embodiments, one magnetic field is generated by a field coil in the electrode near the arcing surface, preferably in the tip of the electrode, and the other magnetic field is produced by either a solenoid adjacent the furnace wall or the mold or crucible or a concentrated relatively short field coil having a number of wound electrically conducting layers insulated from each other.

Where the magnetic field generated by means within the tip is in polarity opposition to the magnetic field generated by the solenoid or another coil adjacent the furnace wall, and where the tip is generally annular and generally U-shaped in cross-section with the electrode field coil disposed within the tip, the normal magnetic field which would be generated by the coil in the tip alone is shaped by mutual interaction with the additional magnetic field in the same volume of space whereby the resultant magnetic field adjacent the arcing surface is more uniform in direction in that it more closely follows the contour of the arcing surface and its capability in rotating the arc while its in a constricted mode is greatly increased. If the relative strengths and magnetic polarities of the tip magnetic field and external magnetic field are adjusted to accomplish this specific result, the magnetic field extending over substantially all portions of the arcing surface of the tip may be nearly of substantially uniform strength as modified by the d) BA equation; as the strength of the tip field is increased with respect to that of the solenoid field, the field strength between the tip and the surface of the melt isincreased with the magnetic field lines extending between the electrode and the melt focusing the arc on the melt which tends to rotate the center of the melt in the opposite direction from that in which the arc rotates; the remainder of the melt outside of the influence of the tip field may rotate in the same direction as the arc rotates, giving greatly improved mixing. The abovedescribed rotational effect is produced only while the fields are in opposition. The tip field and external field are in some other applications or during certain portions of a melting operation caused to be of such polarity that they add to each other; the shape of the resultant magnetic field within the furnace and adjacent the electrode provides for focusing the are on the arcing surface but with less moving force on the arc and is especially suitable for use under certain conditions.

BRIEF DESCRIPTION OF THE DRAWINGS For a better understanding of the invention, refer ence may be had to the perferred embodiment exemplary of the invention shown in the accompanying drawings, in which; 7

FIG. 1 shows a partial sectional elevation of a typical magnetic field pattern produced by a prior art electrode in which there is a magnetic field coil within a tip which is generally annular in shape and generally U- shaped in cross-section;

FIG. 2 shows the magnetic field configuration produced within a furnace by a concentrated coil near or adjacent the furnace wall;

FIG. 3 shows the resultant magnetic field configuration where a tip field and an externally produced field produced by a compact coil outside the fumace' wall are in magnetic polarity opposition within the furnace;

FIG. 4 shows a resultant magnetic field configuration where the externally produced magnetic field and the tip field are in polarity adding and the externally produced magnetic field is generated by a compact field coil disposed near the wall of the furnace;

FIG. 4A illustrates simplified electrical circuit 'diagrams for reversing the magnetic polarity of the tip field, that of the solenoid or concentrated coil field, and those of two fields with respect to each other;

FIG. 5 shows the resultant magnetic field configuration where the magnetic field generated in the electrode tip and an externally produced solenoid field are in polarity opposition;

FIG. 7 also illustrates the resultant magnetic fieldwhere the tip field and the externally produced solenoid field are in polarity opposition, and the strength of the tip field has been further additionally substantially increased relative to the strength of the solenoid field;

FIG. 8 is an illustration of the resultant magnetic field where the tip field generated within the electrode and the externally produced solenoid field are adding at the center line of the furnace;

FIG. 9 is a schematic electrical circuit diagram for automatically reducing the strength of the tip field a certain time after the are starts, and for other purposes;

FIG. 10 shows both a solenoid and an axially adjustable compact field coil adjacent the solenoid for setting up two separately generated external magnetic fields which interact with each other, and one or both of which further interact with the magnetic field generated by a coil in the tip of the electrode;

FIG. 11 shows furnace apparatus in which both a solenoid field which extends above the electrode tip and preferably to the bottom of the melt is used in addition to another magnetic field generated by a concentrated coil having its position axially adjustable along the length of the solenoid to provide a resultant magnetic field within the melt, which gives improved furnace performance in a number of ways, the are being illustrated as diffused;

FIG. 12 shows a diffused are which would extend from a fluid cooled tip having no field coil therein to a melt;

FIG. 13 illustrates the effect of the important formula 4 FIG. 14 is a view of a further embodiment of my invention employing a mold with a retractable bottom, and showing other novel features;

FIG. 15 illustrates a cusp magnetic field which may be produced in the apparatus of FIG. 14 under certain conditions under the control of an operator of the apparatus;

FIG. 16 illustrates a cross-sectional view of furnace apparatus utilizing two electrodes;

FIG. 17 illustrates a resultant magnetic field configuration which may exist in a plane passing through the two electrodes in the two electrode apparatus of FIG. 16, or which may exist in a plane passing through any two electrodes in the three electrode apparatus of FIG. 18; and

FIG. 18 illustrates a cross-sectional view of an embodiment of the invention in a furnace employing three electrodes.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring now to the drawings and FIG. 1 in particular, an electrode generally designated 14 has a supporting column 15 and a tip 16 secured to the supporting column 15 and forming an arcing surface 17. The electrode 14 is shown oriented or disposed with reference to what may be a generally cylindrical furnace wall or a mold 19. Only one half of the cross section in elevation of the electrode 14 is shown for simplicity of illustration, it being understood that the other half of the electrode (not shown) is generally symmetrical with that shown. The longitudinal axis of the electrode is shown by the dashed line 14a which may also be the centerline of the furnace. It will be understood that the supporting column 15 is comprised at least partially of electrically conductive material; is adapted to be connected to a terminal of one polarity of a source of electrical potential to produce and sustain an are 96 between the electrode tip l6 at the arcing surface 17 and the surface of opposite polarity 97. The electrode tip may conveniently be generally U-shaped in cross section as shown in elevation, with an annular space therein in which is disposed a magnetic field coil 18 for setting up or producing the magnetic field shown. It will further be understood that the electrode tip may have a passageway therein, not shown, which may be generally U-shaped in cross section extending around the entire perimeter of the tip through which cooling fluid may pass to remove heat flux from the arcing surface 17 and tip 16, and it will be further understood that the supporting column 15 may have fluid passageways therein opening into the passageways in the tip 16 for bringing cooling fluid to the tip 16 and conducting fluid from the tip 16, these fluid passageways in the supporting column not being shown for convenience of illustration. It will be understood that the passageway in the electrode 14 for the flow of cooling fluid may comprise two semicircular parallel paths as taught for example in US. Pat. No. 3,316,444, issued on Apr. 25, 1967 to R. M. Mentz entitled Arc Heater for Use with Three Phase Alternating Current Source and Chamber and Electrode Structure, and assigned to the assignee of the instant invention. Portions of the aforedescribed electrode 14 may be considered as part of the prior art; an electrode similar to that described in US. Pat. No. 3,369,067, issued Feb. 13, 1968 to S. M. DeCorso for Non-Consumable Annular Fluid Cooled Electrode for Arc Furnaces, or an electrode similar to that described in U.S. Pat. No. 3,369,068, issued to P. F. Kienast for Steam Bleeding in Metal Electrode Arc Furnace, or an electrode similar to that described in US. Pat. No. 3,476,861, issued to Charles B. Wolf for Insulating Non-Consumable Arc Electrode, the above patents being assigned to the assignee of the instant invention, may be employed as the electrode shown in FIG. 1, all of the electrodes in the referenced patents having a magnetic field coil in the tip or close to the arcing surface, and a fluid passageway in the tip for conducting heat flux away from the arcing surface.

In FIG. 1, flux lines of the magnetic field previously alluded to and set up by the electrode tip field coil 18 are shown at 71 to 79, inclusive, and follow the classical pattern of a magnetic field set up by a solenoid having a length which is small relative to its diameter; the electromagnetic field shown is exemplary only, since it represents a field produced by a noncritical excitation which may be varied at the will of a user of the apparatus.

It is noted that all of the lines 71 to 79 extend generally away from the field coil 18 toward the wall 19 of the furnace or mold.

The lines 80 to 94, inclusive, extending toward the longitudinal axis of the electrode by their relative spacing indicate the portion of the total magnetomotive force generated which is required to set up a magnetic field in the axial area between adjacent lines; as would be expected, the lines are closely spaced within the coil indicating that a considerable portion of the total magnetomotive force is required to force the field through the interior of the solenoid, the lines becoming progressively more distant from an adjacent line on each side thereof as the axial distance from the coil increases.

An arc is shown at 96 between the arcing surface 117 and the upper surface of the melt 97, it being understood that the melt may be comprised or composed at least partially of electrically conductive material and may form a surface of polarity opposite that of the tip; it is seen that several of the magnetic field lines traverse the path of are 96, lines 71, 72 and 73, for example, and while the magnetic field lines do not follow the contour of the arcing surface and are not completely perpendicular to the arc path 96, by Fleming's rule relating current direction, magnetic field direction and conductor or arc movement direction, components of force are exerted on the arc 96 which cause it to move substantially continuously in an annular path around the electrode and between the electrode 14 and the melt 97. To some extent under assumed conditions, the are 96 would tend to follow the magnetic field lines and to be focused thereby so that the are 96 may be thought of as slanting somewhat outwardly from the longitudinal axis 14a.

Table I entitled Magnetic Field Values for Electrode Field Coil," which follows, shows calculations of the magnitude of the magnetic field vector in gausses, and the angle of the field vector measured from the axis 14a in degrees, for 10 axial positions of 9 inches to 18 inches, inclusive, at a field radial position of 0.1 inch (the electrode axis 14a represents 0.0 inch), 10 similar axial positions at a field radial position of 1.0 inches, ten similar axial positions at a field radial position of 2.0 inches, ten similar axial positions at a field radial position of 3.0 inches, ten similar axial positions at a field radial position of 4.0 inches, 10 similar axial positions at a field radial position of 5.0 inches, ten similar axial positions at a field radial position of 6.0 inches, and 10 similar axial positions at a field radial position of 7.0 inches.

The Table 1 shows that the electrode tip field coil excitation force was 8,000 ampere turns, that its axial location or extension was substantially 16.6 to 17.8 inches, and that its radial position or extension from the axis of the electrode was substantially 1.325 to 1.675 inches, which gives an indication of its length and inside and outside diameters.

The zero inch axial position may correspond to the bottom of the furnace or mold, or may be a selected point distant from the field coil. In Table I, all of the repetitive radial position field values made at an axial position of 17.0 inches would represent measurements made in a plane passing through the field coil 18 and extending perpendicular to the longitudinal axis of the electrode.

The values of the magnitude of the magnetic field vector and the angle of the magnetic field vector to the axis are those of a magnetic field which can be employed in my invention; they will become more meaningful hereinafter where additional figures of the drawings are discussed which disclose a resultant field pattern produced by the mutual interaction of two or more independently generated magnetic fields, but it is to be understood that my invention is not limited to the use of a field having the precise values shown in Table 1 or those of any of the other tables to follow.

TABLE 1 MAGNETIC FIELD VALUES FOR ELECTRODE FIELD COIL Electrode Field Coil Excitation 8000 amp.

turns Electrode Field Coil Location Axial 16.6 to 17.8 inches Radial 1.325 to 1.675 inches Field Points Axial Radial Magnitude of Anglc of Field Position Position Field Vector Vector to Axis (inches) (inches) (gauss) (Degrees) 9 0.1 7.9 178.98 10 0.1 11.5 178.84 11 0.1 17.8 178.67 12 0.1 29.3 178.45 13 0.1 53.0 178.14 14 0.1 108.3 177.74 15 0.1 257.8 177.30 16 0.1 665.7 177.51 17 0.1 11618 179.52 18 0.1 9063 181.86 

1. An electric arc furnace apparatus comprising a furnace vessel adapted to receive at least partially electrically condUctive material to be heated to form a melt, a substantially nonconsumable electrode, means for mounting the electrode in predetermined position with respect to the vessel, the electrode including means forming an arcing surface and means within the electrode mounted near the arcing surface for generating a first magnetic field with a portion of said first magnetic field existing in the space external to the electrode and near the arcing surface, the electrode and the material to be melted being adapted to be electrically connected to terminals of opposite polarity of a source of electrical potential to produce and sustain an electric arc therebetween, an axially disposed concentrated electrical coil mounted in a predetermined position with respect to the furnace vessel for generating an additional magnetic field within at least a portion of the volume of the vessel, the electrode being so mounted with respect to the means for generating an additional magnetic field that the magnetic poles of the first magnetic field lie in a line substantially parallel to a line passing through the additional magnetic field, the first magnetic field and the additional magnetic field being capable of being selectively in polarity adding or in polarity opposition, both the first magnetic field and the additional magnetic field being generated in at least that portion of the volume of the vessel which includes the area near the arcing surface and at least a portion of the space between the arcing surface and the material to be melted, the first and additional magnetic fields by mutual interaction in said last named portion of the volume of the vessel at at least one predetermined point in that volume which is significantly closer to said arcing surface than to both said furnace wall and said melt producing a resultant magnetic field which will, depending upon the relative strength and polarity of said first magnetic field over those of said additional magnetic fields, have a strength and orientation in said volume which is either substantially transverse to the arc and especially adapted to rotate the arc or which is substantially parallel to the arc and especially adapted to focus the arc and to stir the melt.
 2. Electric arc furnace apparatus according to claim 1 in which the arc extends substantially parallel to the axis of the vessel in a path between the electrode and the material to be melted, in which the two fields are in polarity opposition for at least a portion of the time of operation along lines parallel to said vessel axis and the resultant field has a strong component extending radially across the arcing surface, said component being generally transverse to the arc path and exerting a force on the arc which causes the arc to move substantially continuously around a closed track formed by the arcing surface, the movement of the arc reducing the rate of erosion of material from the arcing surface as a result of arc action thereon.
 3. Electric arc furnace apparatus according to claim 2 including means for reversing the relative polarity of one magnetic field with respect to the other after at least a portion of the material to be melted has been reduced to a molten condition whereby the two magnetic fields are then in polarity adding, and means for adjusting the strength of one magnetic field relative to the strength of the other field whereby a resultant field is produced with a strong component extending between said electrode and said melt and at least to some depth within the melt, said last named component focusing the arc between said electrode and said melt and by interaction with current filaments in the melt extending from the site of the arc spot thereon assisting in stirring the melt.
 4. Electric arc furnace apparatus according to claim 2 including means for adjusting the strength of at least one magnetic field relative to the other whereby the relative strengths of the two magnetic fields are so adjusted with respect to each other that the resultant field extends radiAlly across the arcing surface and substantially follows the contour of the arcing surface and is substantially parallel to the arcing surface around substantially the entire outside contour thereof.
 5. An electric arc furnace apparatus comprising a furnace vessel adapted to receive at least partially electrically conductive material to be heated to form a melt, an electrode, means for mounting the electrode in predetermined position with respect to the vessel, the electrode including means forming an arcing surface and means within the electrode mounted near the arcing surface for generating a first magnetic field, a portion of which exists in the space external to the electrode and near the arcing surface, the electrode and the material to be melted being adapted to be electrically connected to terminals of opposite polarity of a source of electrical potential to produce and sustain an electric arc therebetween, said furnace having a wall comprised of non-ferromagnetic material, an elongated solenoid mounted adjacent the wall of the furnace for generating an additional magnetic field within at least a portion of the volume of the vessel, the solenoid extending axially upward to a position at least above the highest axial position of the electrode tip, the solenoid extending axially downward to a position below the lowest level of the melt formed by the melting of the material initially placed in the furnace, the electrode being so mounted with respect to the solenoid that the magnetic poles of the first magnetic field lie in a line substantially parallel to a line passing through the magnetic poles of the additional magnetic field, the first magnetic field and the additional magnetic field being selectively in polarity adding or in polarity opposition, both the first magnetic field and the additional magnetic field being generated in at least that portion of the volume of the vessel which includes the area near the arcing surface and at least a portion of the space between the arcing surface and the material to be melted, the first and additional magnetic fields by mutual interaction in said last named portion of the volume of the vessel at at least one predetermined point in that volume which is significantly closer to said arcing surface than to both said furnace wall or said melt producing a resultant magnetic field having a configuration especially suited to control the arc in a manner to give improved furnace performance, said first magnetic field being substantially stronger than said additional magnetic field produced by said solenoid.
 6. Electric arc furnace apparatus according to claim 1 in which the wall of the furnace comprises non-ferromagnetic material and in which said compact coil is mounted at a predetermined axial position adjacent the wall of the furnace.
 7. Electric arc furnace apparatus according to claim 6 in which said compact coil is mounted at an axial position adjacent the wall of the furnace substantially corresponding to the axial position of the tip of the electrode within the furnace.
 8. Electric arc furnace apparatus according to claim 6 in which the axial position of said compact coil is adjustable.
 9. Electric arc furnace apparatus according to claim 7 in which said magnetic field coil in the electrode and said compact coil are so energized with respect to each other that their magnetic fields are in magnetic polarity opposition along the axis of the electrode and along the centerline of the furnace.
 10. An electric arc furnace apparatus comprising a furnace vessel adapted to receive at least partially electrically conductive material to be heated to form a melt, an electrode, means for mounting the electrode in predetermined position with respect to the vessel, the electrode including means forming an arcing surface and means within the electrode mounted near the arcing surface for generating a first magnetic field, a portion of which exists in the space external to the electrode and near the arcing surface, the electrode And the material to be melted being adapted to be electrically connected to terminals of opposite polarity of a source of electrical potential to produce and sustain an electric arc therebetween, said furnace having a wall comprised of non-ferromagnetic material, an elongated solenoid mounted adjacent the wall of the furnace for generating an additional magnetic field within at least a portion of the volume of the vessel, the solenoid extending axially upward to a position at least above the highest axial position of the electrode tip, the solenoid extending axially downward to a position below the lowest level of the melt formed by the melting of the material initially placed in the furnace, the electrode being so mounted with respect to the solenoid that the magnetic poles of the first magnetic field lie in a line substantially parallel to a line passing through the magnetic poles of the additional magnetic field, the first magnetic field and the additional magnetic field being selectively in polarity adding or in polarity opposition, both the first magnetic field and the additional magnetic field being generated in at least that portion of the volume of the vessel which includes the area near the arcing surface and at least a portion of the space between the arcing surface and the material to be melted, the first and additional magnetic fields by mutual interaction in said last named portion of the volume of the vessel at at least one predetermined point in that volume which is significantly closer to said arcing surface than to both said furnace wall or said melt producing a resultant magnetic field having a configuration especially suited to control the arc in a manner to give improved furnace performance, said first magnetic field being substantially stronger than said additional magnetic field produced by said solenoid, a compact field coil mounted adjacent the solenoid and having an axially adjustable position thereon, a magnetic yoke enclosing the ends and the outside of the compact coil and providing a low reluctance path, and means for energizing the compact coil to produce a third magnetic field in at least a portion of the volume of the furnace, said resultant magnetic field configuration in the furnace being produced by the mutual interaction of at least one said field with any other said field.
 11. Electric arc furnace apparatus according to claim 10 in which the axial position of the compact coil and yoke is adjusted with respect to the level of the melt whereby a strong component of the resultant field exerts a stirring force on the melt.
 12. Electric arc furnace apparatus according to claim 11 and including in addition means for substantially continually feeding material into the furnace to form an ingot, the stirring force produced by said strong component of the resultant field permitting an increased feed rate with more rapid heating and dispersion of the fed material, improved grain structure and a more nearly homogeneous ingot.
 13. Electric arc furnace apparatus according to claim 10 including means for reversing the relative polarity of one magnetic field with respect to the other and means for adjusting the strength of one magnetic field relative to the other, the resultant magnetic field produced by mutual interaction of the field produced by the coil in the electrode and the field produced by the solenoid is shaped by adjustment of the relative strengths of said two fields and the selection of their relative magnetic polarities to have at least one strong component effective for rotating and focusing the arc, the relative axial position of the compact coil and yoke selected to provide a magnetic field for stirring the melt.
 14. An electric arc furnace apparatus comprising a furnace vessel adapted to receive at least partially electrically conductive material to be heated to form a melt, an electrode, means for mounting the electrode in predetermined position with respect to the vessel, the electrode including means forming an arcing surface and means within the electrode mounted near the arcing surface for generating a first magnetic field, a portion of which exists in the space external to the electrode and near the arcing surface, the electrode and the material to be melted being adapted to be electrically connected to terminals of opposite polarity of a source of electrical potential to produce and sustain an electric arc therebetween, said furnace having a wall comprised of non-ferromagnetic material, an elongated solenoid mounted adjacent the wall of the furnace for generating an additional magnetic field within at least a portion of the volume of the vessel, the solenoid extending axially upward to a position at least above the highest axial position of the electrode tip, the solenoid extending axially downward to a position below the lowest level of the melt formed by the melting of the material initially placed in the furnace, the electrode being so mounted with respect to the solenoid that the magnetic poles of the first magnetic field lie in a line substantially parallel to a line passing through the magnetic poles of the additional magnetic field, the first magnetic field and the additional magnetic field being selectively in polarity adding or in polarity opposition, both the first magnetic field and the additional magnetic field being generated in at least that portion of the volume of the vessel which includes the area near the arcing surface and at least a portion of the space between the arcing surface and the material to be melted, the first and additional magnetic fields by mutual interaction in said last named portion of the volume of the vessel at at least one predetermined point in that volume which is significantly closer to said arcing surface than to both said furnace wall or said melt producing a resultant magnetic field having a configuration especially suited to control the arc in a manner to give improved furnace performance, said additional magnetic field produced by said solenoid being substantially stronger than said first magnetic field.
 15. An electric arc furnace apparatus comprising a furnace vessel adapted to receive at least partially electrically conductive material to be heated to form a melt, an electrode, means for mounting the electrode in predetermined position with respect to the vessel, the electrode including means forming an arcing surface and means within the electrode mounted near the arcing surface for generating a first magnetic field, a portion of which exists in the space external to the electrode and near the arcing surface, the electrode and the material to be melted being adapted to be electrically connected to terminals of opposite polarity of a source of electrical potential to produce and sustain an electric arc therebetween, said furnace having a wall comprised of non-ferromagnetic material, an elongated solenoid mounted adjacent the wall of the furnace for generating an additional magnetic field within at least a portion of the volume of the vessel, the solenoid extending axially upward to a position at least above the highest axial position of the electrode tip, the solenoid extending axially downward to a position below the lowest level of the melt formed by the melting of the material initially placed in the furnace, the electrode being so mounted with respect to the solenoid that the magnetic poles of the first magnetic field lie in a line substantially parallel to a line passing through the magnetic poles of the additional magnetic field, the first magnetic field and the additional magnetic field being selectively in polarity adding or in polarity opposition, both the first magnetic field and the additional magnetic field being generated in at least that portion of the volume of the vessel which includes the area near the arcing surface and at least a portion of the space between the arcing surface and the material to be melted, the first and additional magnetic fields by mutual interaction in said last named portion of the volume of the vessel at at least one predetermineD point in that volume which is significantly closer to said arcing surface than to both said furnace wall or said melt producing a resultant magnetic field having a configuration especially suited to control the arc in a manner to give improved furnace performance, said first magnetic field being substantially stronger than said additional magnetic field produced by said solenoid, a compact field coil mounted adjacent the solenoid and having an axially adjustable position thereon, a magnetic yoke enclosing the ends and the outside of the compact coil and providing a low reluctance path, and means for energizing the compact coil to produce a third magnetic field in at least a portion of the volume of the furnace, said resultant magnetic field configuration in the furnace being produced by the mutual interaction of at least one said field with any other said field.
 16. Electric arc furnace apparatus according to claim 15 in which the axial position of the compact coil and yoke is adjusted with respect to the level of the melt whereby a strong component of the resultant field exerts a stirring force on the melt.
 17. Electric arc furnace apparatus according to claim 16 including in addition means for substantially continually feeding material into the furnace to form an ingot, the stirring force produced by said strong component of the resultant field permitting an increased feed rate with more rapid heating and dispersion of the fed material, improved grain structure and a more nearly homogeneous ingot.
 18. Electric arc furnace apparatus according to claim 15 in which the resultant magnetic field produced by mutual interaction of the field produced by the coil in the electrode and the field produced by the solenoid is shaped by adjustment of the relative strengths of said two fields and the selection of their relative magnetic polarities to have at least one strong component effective for rotating and focusing the arc, the relative axial position of the compact coil and yoke being selected to provide a magnetic field for stirring the melt.
 19. Electric arc furnace apparatus comprising a furnace vessel adapted to receive at least partially electrically conductive material to be heated to form a melt, an electrode, means for mounting the electrode in predetermined position with respect to the vessel, the electrode including means forming an arcing surface and means within the electrode mounted near the arcing surface for generating a first magnetic field a portion of which exists in the space external to the electrode and near the arcing surface, the electrode and the material to be melted being adapted to be electrically connected to terminals of opposite polarity of a source of electrical potential to produce and sustain an electric arc therebetween, first and second means mounted in predetermined position with respect to the furnace vessel for generating a first additional magnetic field and a second additional magnetic field respectively within the vessel, the first and first and second additional magnetic fields by mutual interaction in the vessel producing a resultant magnetic field having a configuration especially suited to control the arc in a manner to give improved furnace performance.
 20. The combination as claimed in claim 19 wherein said furnace vessel comprises ferromagnetic material.
 21. The combination as claimed in claim 19 wherein said furance vessel comprises nonmagnetic material.
 22. Electric arc furnace apparatus comprising a furnace vessel adapted to receive at least partially electrically conductive material to be heated to form a melt, an electrode, means for mounting the electrode in predetermined position with respect to the vessel, the electrode including means forming an arcing surface and means within the electrode mounted near the arcing surface for generating a first magnetic field, a portion of which exists in the space external to the electrode and near the arcing surface, the electrode and the material to be melted being adApted to be electrically connected to terminals of opposite polarity of a source of electrical potential to produce and sustain an electric arc therebetween, a solenoid and compact coil mounted in a predetermined position with respect to the furnace vessel for generating a first additional magnetic field and a second additional magnetic field respectively within at least a portion of the volume of the vessel, the first magnetic field and the first and second additional magnetic fields being generated in at least that portion of the volume of the vessel which includes the area near the arcing surface and at least a portion of the space between the arcing surface and the material to be melted, the first and second additional magnetic fields by mutual interaction in said last named portion of the volume of the vessel producing a resultant magnetic field having a configuration especially suited to control the arc in a manner to give improved furnace performance.
 23. Electric arc furnace apparatus comprising a furnace vessel adapted to receive at least partially electrically conductive material to be heated to form a melt, an electrode, means for mounting the electrode in predetermined position with respect to the vessel, the electrode including means forming an arcing surface and means within the electrode mounted near the arcing surface for generating a first magnetic field a portion of which exists in the space external to the electrode and near the arcing surface, the electrode and the material to be melted being adapted to be electrically connected to terminals of opposite polarity of a source of electrical potential to produce and sustain an electric arc therebetween, first and second means mounted in a predetermined position with respect to the furnace vessel for generating a first additional magnetic field and a second additional magnetic field respectively within at least a portion of the volume of the vessel, the first magnetic field and the first and second additional magnetic fields being generated in at least that portion of the volume of the vessel which includes the area near the arcing surface and at least a portion of the space between the arcing surface and the material to be melted, the first and second additional magnetic fields by mutual interaction in said last named portion of the volume of the vessel producing a resultant magnetic field having a configuration especially suited to control the arc in a manner to give improved furnace performance, said furnace vessel comprising ferromagnetic material, said first and said second additional magnetic fields being in polarity opposition with respect to each other.
 24. Electric arc furnace apparatus comprising a furnace vessel adapted to receive at least partially electrically conductive material to be heated to form a melt, an electrode, means for mounting the electrode in predetermined position with respect to the vessel, the electrode including means forming an arcing surface and means within the electrode mounted near the arcing surface for generating a first magnetic field a portion of which exists in the space external to the electrode and near the arcing surface, the electrode and the material to be melted being adapted to be electrically connected to terminals of opposite polarity of a source of electrical potential to produce and sustain an electric arc therebetween, first and second means mounted in a predetermined position with respect to the furnace vessel for generating a first additional magnetic field and a second additional magnetic field respectively within at least a portion of the volume of the vessel, the first magnetic field and the first and second additional magnetic fields being generated in at least that portion of the volume of the vessel which includes the area near the arcing surface and at least a portion of the space between the arcing surface and the material to be melted, the first and second additional magnetic fields by mutual interaction in said last named portion of the volume of the vessel prOducing a resultant magnetic field having a configuration especially suited to control the arc in a manner to give improved furnace performance, said furnace vessel comprising ferromagnetic material, said first and said second additional magnetic fields being in polarity addition with respect to each other.
 25. Electric arc furnace apparatus including in combination, a mold having a substantially cylindrical wall adapted to receive at least partially conductive material to be melted, a substantially nonconsumable electrode mounted in the mold and extending axially therein, the electrode and the material to be melted being adapted to be connected to terminals of opposite polarity of a source of potential to produce and sustain an arc therebetween, a first magnetic field generating means mounted outside of the wall of the furnace and means for energizing said first magnetic field generating means, a second magnetic field generating means mounted outside of the wall of the furnace and means for energizing said second magnetic field generating means, said first and second magnetic field generating means interacting within said furnace to give improved furnace performance.
 26. Electric arc furnace apparatus according to claim 25 including means for substantially continually feeding additional material to the melt therein to form an ingot.
 27. Electric arc furnace apparatus according to claim 25 including means for evacuating the furnace to a preselected pressure therein.
 28. Electric arc furnace apparatus including in combination, a mold having a substantially cylindrical wall composed of diamagnetic material and adapted to receive at least partially conductive material to be melted, an electrode mounted in the mold and extending axially therein, the electrode and the material to be melted being adapted to be connected to terminals of opposite polarity of a source of potential to produce and sustain an arc therebetween, an elongated solenoid mounted adjacent the wall of the furnace, means for energizing the solenoid, a concentrated magnetic field coil mounted adjacent the solenoid and having an axially adjustable position therealong, a magnetic yoke enclosing the ends and at least a partion of the outside of the concentrated coil and forming a low reluctance path, and means for energizing the concentrated coil, the axial position of the concentrated coil and yoke being selected whereby a resultant magnetic field in at least a portion of the volume of the furnace resulting from the mutual interaction of the magnetic field generated by the solenoid and the magnetic field generated by the concentrated coil has a predetermined field configuration useful in improving the operation of the furnace.
 29. The method of operating an electric arc furnace including the steps of producing an electric arc between an electrode and conductive material to be melted to form a melt, energizing a tip field coil in said electrode tip to produce a first magnetic field, generating a second magnetic field having a characteristic of the magnetic field of a compact coil within at least a portion of the volume of the furnace which magnetic field lines extending substantially axially through the furnace between the electrode tip and the surface of the melt, interacting the first and second magnetic fields at at least one predetermined point significantly closer to said arcing surface than to both said furnace wall or said melt to produce a resultant magnetic field adjacent the arcing surface and between the arcing surface and the surface of the melt which will, depending upon the relative strength and polarity of said first magnetic field and said second magnetic field, have a strength and orientation which may be alternately substantially transverse to said arc and especially suited to rotate the arc or which may be substantially parallel to the arc and especially suited to focus the arc and stir the melt.
 30. A method of operating an electric arc furnace having a wall and adapted to receiVe conductive material to be melted to form a melt which comprises producing an electric arc between the material and an electrode spaced from the surface thereof, generating a first magnetic field by means in the electrode, generating a second magnetic field by means external to the electrode, the two magnetic fields interacting in a field interaction zone adjacent the electrode with a resulting distortion of both magnetic field patterns at at least one predetermined point significantly closer to said arcing surface than to both said furnace wall or said material and the production of a resultant magnetic field which will, depending upon the relative strength and polarity of said first magnetic field and said second magnetic field have a strength and orientation which may be alternately substantially transverse to said arc and especially suited to rotate the arc or which may be substantially parallel to the arc and especially suited to focus the arc and stir the material, the relative strength of said second magnetic field being substantially different than the relative strength of said first magnetic field in said field interaction zone.
 31. A method according to claim 30 including the step of moving the arc around a closed arc track on said arcing surface substantially continuously.
 32. A method according to claim 31 in which said first and second fields are in polarity adding and the strength of the first magnetic field generated in the electrode is substantially larger relative to the strength of the second magnetic field whereby the resultant magnetic field includes magnetic field lines which extend between the electrode and the surface of the melt at an oblique angle with respect to the axis of the electrode around the entire periphery of the electrode, said lastnamed magnetic field lines tending to focus the arc between the electrode and the melt.
 33. A method according to claim 31 in which said field interaction zone adjacent the electrode is produced by generating the magnetic field in the tip and the externally produced magnetic field in magnetic polarity opposition with respect to each other along an axis substantially coinciding with an axis of the electrode.
 34. A method according to claim 30 in which the furnace is generally cylindrical with a wall composed of diamagnetic material and the externally produced magnetic field is produced by a solenoid adjacent at least a portion of said furnace wall.
 35. A method according to claim 31 in which the externally produced magnetic field is produced by a solenoid adjacent at least a portion of said wall.
 36. A method according to claim 30 including the additional step of continually feeding additional material to the melt and adjusting the position of the electrode as the level of the melt rises to maintain a substantially constant arc length between the electrode and the melt, and in which said externally produced magnetic field is additionally characterized as having magnetic field lines which would normally extend axially through the furnace to a position above any poistion attained by the electrode and to a position below any level reached by the level of the melt in the absence of field distortion by the separately generated magnetic field in said electrode.
 37. A method according to claim 31 including the additional step of continually feeding material to the melt in the furnace and repeatedly adjusting the position of the electrode as the level of the melt rises to maintain a substantially constant arc length between the electrode and the melt, and in which the externally produced magnetic field is additionally characterized as normally, in the absence of a distorting magnetic field produced in the electrode having lines which extend substantially axially through the furnace to a position above the highest position reached by the electrode and to a position below the lowest position attained by the surface of the melt.
 38. A method according to claim 30 in which the field produCed in the electrode and the externally produced field are in adding magnetic polarity.
 39. The method according to claim 30 in which the field produced in the electrode and the externally produced field are in opposing magnetic polarity.
 40. The method of operating an electric arc furnace having a furnace wall, adapted to receive at least partially conductive material to be melted which comprises producing an electric arc between the electrode and the material to be melted to reduce the material to a molten state, generating a first magnetic field within the tip, generating a second magnetic field within the furnace by independent field generating means disposed adjacent the wall of the furnace, the first and second magnetic fields interacting to produce a resultant field in the furnace in the volume thereof encompassing the electrode tip and extending to the surface of the melt, the resultant magnetic field controlling the arc to provide improved furnace operation, and utilizing a concentrated field coil with a yoke of magnetic material therearound, a portion thereof, disposed external to the second field generating means for independently creating within the furnace a third magnetic field in the portion of the volume of the furnace occupied by the melt, said third magnetic field being selectively in magnetic polarity opposition or magnetic polarity adding with respect to the second generated magnetic field, the additional resultant magnetic field pattern produced by interaction of the second and third magnetic fields providing improved furnace operation.
 41. A method according to claim 40 in which the concentrated coil and the magnetic yoke therearound are additionally characterized as having their axial positions adjustable along the length of the second magnetic field producing means to control the furnace operation in at least one aspect to increase the stirring of the melt and increase the rate dispersion of additional material fed to the melt while in a relatively upper position along said axial length of the second magnetic field producing means, and while in a relatively lower axial position to have less effect on stirring the melt but an increased effect on the grain structure of an ingot formed in the furnace.
 42. A method according to claim 40 including the additional step of evacuating the furnace to a sufficiently low pressure wherein a diffused arc discharge occurs between the electrode and the melt.
 43. The method of operating an electric furnace according to claim 40 in which said furnace wall comprises primarily dielectric material.
 44. The method of operating an electric arc furnace adapted to receive at least partially conductive material to be melted and adapted to have a controlled atmosphere therein comprising the steps of producing an arc between an electrode and the melt while maintaining the pressure within the furnace at a sufficiently low value whereby the arc goes into a diffused mode of operation, utilizing a solenoid adjacent the wall of the furnace and extending substantially from the bottom thereof to a position higher than that reached by the electrode as the position of the electrode is adjusted as the level of the melt increases to maintain a substantially constant arc length between the electrode and the melt, the magnetic field lines of the solenoid normally extending in a generally axial direction through the volume of the furnace and adjacent the electrode and between the electrode and the melt, said lines assisting in preventing an arc from striking from the electrode to the wall of the furnace and assisting in focusing the arc between the electrode and the melt, said lines tending to produce movement within the melt resulting in increased heating efficiency and more rapid dispersion of material in the melt thereby increasing the feed rate of material to the melt, and utilizing a compact magnetic field coil having a magnetic yoke therearound with a position adjustable axially along the length of the solenOid, moving the concentrated coil to an axial position adjacent the bottom of the melt to improve the grain structure of an ingot formed by the solidified portion of the material to be melted and improve the homogeneity of the ingot, and moving the concentrated coil to a position axially nearer to the surface of the melt, the concentrated field coil in said last-named position assisting in controlling the arc and assisting in improving the heating efficiency of the furnace.
 45. A method according to claim 61 in which the magnetic field produced by the solenoid and the magnetic field produced by the concentrated coil are in magnetic polarity opposition.
 46. A method according to claim 44 wherein the magnetic field produced by the solenoid and the magnetic field produced by the concentrated coil are in magnetic polarity adding.
 47. The method according to claim 45 including the additional step of fluid cooling the arcing surface of the electrode to assist in reducing the rate of the erosion of material therefrom.
 48. The method of operating an electric arc furnace to form an ingot composed of at least partially electrically conductive material which includes the steps of placing an initial amount of material in a mold, mounting an electrode within the furnace in spaced position with respect to the material, the electrode having a tip forming an arcing surface and a magnetic field coil therein close to the arcing surface, energizing the field coil to generate a first magnetic field, energizing an elongated solenoid mounted near the wall of the mold to generate a second magnetic field with magnetic field lines normally extending axially through the furnace, creating an arc between the electrode and the material, adjusting the energization of the solenoid whereby the strength of the magnetic field of the solenoid is relatively great compared to that of the tip field coil and a resultant magnetic field is produced by mutual interaction of the two magnetic fields which has a strong vertical component and maintaining said adjustment while the pool is shallow to exert large rotational forces on the material of the pool, and thereafter after the pool has become deeper with the fields in polarity adding increasing the strength of the tip-generated field with respect to the solenoid-generated field to decrease the vertical field component of the resultant field. 